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Technical Note—Minimizing Average Flow Time with Parallel Machines

Author

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  • W. A. Horn

    (National Bureau of Standards, Washington, D.C.)

Abstract

This note shows that the assignment and sequencing of single-operation jobs in a parallel-machine environment can be formulated as an assignment problem. Means for reducing the size and computational difficulty of this problem are identified.

Suggested Citation

  • W. A. Horn, 1973. "Technical Note—Minimizing Average Flow Time with Parallel Machines," Operations Research, INFORMS, vol. 21(3), pages 846-847, June.
    • Handle: RePEc:inm:oropre:v:21:y:1973:i:3:p:846-847
    DOI: 10.1287/opre.21.3.846
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    Cited by:

    1. Jiang, Xiaojuan & Lee, Kangbok & Pinedo, Michael L., 2021. "Ideal schedules in parallel machine settings," European Journal of Operational Research, Elsevier, vol. 290(2), pages 422-434.
    2. Rabia Nessah & Chengbin Chu, 2010. "Infinite split scheduling: a new lower bound of total weighted completion time on parallel machines with job release dates and unavailability periods," Annals of Operations Research, Springer, vol. 181(1), pages 359-375, December.
    3. Cole, Richard & Correa, Jose & Gkatzelis, Vasillis & Mirrokni, Vahab & Olver, Neil, 2015. "Decentralized utilitarian mechanisms for scheduling games," LSE Research Online Documents on Economics 103081, London School of Economics and Political Science, LSE Library.
    4. Lenstra, J. K. & Rinnooy Kan, A. H. G., 1980. "An Introduction To Multiprocessor Scheduling," Econometric Institute Archives 272258, Erasmus University Rotterdam.
    5. T.C. Edwin Cheng & Qing Ding & Mikhail Y. Kovalyov & Aleksander Bachman & Adam Janiak, 2003. "Scheduling jobs with piecewise linear decreasing processing times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(6), pages 531-554, September.
    6. Han Hoogeveen & Petra Schuurman & Gerhard J. Woeginger, 2001. "Non-Approximability Results for Scheduling Problems with Minsum Criteria," INFORMS Journal on Computing, INFORMS, vol. 13(2), pages 157-168, May.
    7. Marcin Siepak & Jerzy Józefczyk, 2014. "Solution algorithms for unrelated machines minmax regret scheduling problem with interval processing times and the total flow time criterion," Annals of Operations Research, Springer, vol. 222(1), pages 517-533, November.
    8. Tjark Vredeveld & Cor Hurkens, 2002. "Experimental Comparison of Approximation Algorithms for Scheduling Unrelated Parallel Machines," INFORMS Journal on Computing, INFORMS, vol. 14(2), pages 175-189, May.
    9. Celia A. Glass & Hans Kellerer, 2007. "Parallel machine scheduling with job assignment restrictions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(3), pages 250-257, April.
    10. Leah Epstein & Ido Yatsiv, 2017. "Preemptive scheduling on uniformly related machines: minimizing the sum of the largest pair of job completion times," Journal of Scheduling, Springer, vol. 20(2), pages 115-127, April.
    11. Zhi-Long Chen & Guruprasad Pundoor, 2006. "Order Assignment and Scheduling in a Supply Chain," Operations Research, INFORMS, vol. 54(3), pages 555-572, June.
    12. Juntaek Hong & Kangbok Lee & Michael L. Pinedo, 2020. "Scheduling equal length jobs with eligibility restrictions," Annals of Operations Research, Springer, vol. 285(1), pages 295-314, February.
    13. Dušan Knop & Martin Koutecký, 2018. "Scheduling meets n-fold integer programming," Journal of Scheduling, Springer, vol. 21(5), pages 493-503, October.
    14. Ali Allahverdi & John Mittenthal, 1994. "Scheduling on M parallel machines subject to random breakdowns to minimize expected mean flow time," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(5), pages 677-682, August.
    15. Felipe T. Muñoz & Guillermo Latorre-Núñez & Mario Ramos-Maldonado, 2023. "Developing New Bounds for the Performance Guarantee of the Jump Neighborhood for Scheduling Jobs on Uniformly Related Machines," Mathematics, MDPI, vol. 12(1), pages 1-16, December.

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